Physics-informed neural networks for exploring soliton collisions in the non-integrable Schamel equation in plasmas

Physics-informed neural networks (PINNs) have achieved the integration of data with mathematical and physical models and have emerged as a popular method for solving partial differential equations. In this paper, we employ the PINN algorithm to numerically solve the non-integrable Schamel equation that arises in plasmas. By embedding the initial-boundary conditions into this non-integrable equation within the PINN framework, we successfully learn the data-driven single-soliton solution and accurately predict three patterns of two-soliton interaction. These results demonstrate the ability of the PINN algorithm to capture complex dynamical behaviors of non-integrable systems and reveal the unique nonlinear characteristics of soliton collisions in the Schamel equation, in accordance with the results of traditional numerical methods. This study not only extends the applicability of the PINN algorithm to explore solitary wave dynamics in non-integrable models, but it also provides key theoretical support for understanding complex physical processes such as ion acoustic waves and electron capture effects in plasmas.